Hotelling

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Hotellings Rule or where P is the net
price (or rent, or royalty) of the resource.
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Intuition behind Hotellings Rule
Owner of financial resources two uses of the
capital
An interest generating financial asset
Invest capital in a mine
Return on mine must also be r in equilibrium
r return per period
As mine is not intrinsically productive, price of
mineral must rise at rate r.
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Hotellings Rule By integration implies
that and so
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Hotellings rule the time path of the resource
net price
Pt
Pt P0e?t
P0
t
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Hotellings rule non-uniqueness of efficient
time paths of the resource net price
Pt
Pt Pbe?t
Pt Pae?t
Pb
Pa
t
The optimal path will be that one which satisfies
S ? 0 as t??
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The time paths of the resource net price and stock
Pt
St
Remaining resource stock
Pt
Net price
P0
t
t
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Hotellings rule with a backstop technology
available
Pt
Choke Price
Pt P0e?t
P0
tT
t
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The time paths of the resource net price and
stock with a backstop technology.
St
Remaining resource stock
Pt
Net price
P0
tT
tT
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• A market economy will probably not deliver an
  efficient and optimal allocation of non-renewable
  resources because
• Monopoly depletion too slow!
• Social costs of resource depletion not
  considered. (e.g. pollution externalities).
• Private (market) interest rate above the social
  discount rate.

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